A339530 Decimal expansion of Sum_{k>=1} (zeta(8*k)-1).

0, 0, 4, 0, 9, 2, 6, 9, 8, 2, 9, 9, 2, 8, 6, 2, 8, 7, 3, 0, 7, 4, 7, 6, 2, 0, 4, 6, 8, 9, 6, 4, 0, 2, 5, 9, 8, 6, 5, 2, 4, 9, 8, 2, 4, 7, 3, 5, 4, 0, 0, 1, 6, 9, 8, 1, 2, 4, 9, 1, 0, 5, 6, 0, 0, 5, 5, 5, 7, 2, 1, 3, 9, 8, 9, 5, 8, 1, 9, 3, 5, 8, 3, 5, 4, 4, 8, 8, 9, 4, 3, 5, 1, 8, 1, 9, 6, 9, 5, 1, 1, 5, 0, 3, 6

Offset: 0

Author

Vaclav Kotesovec, Dec 08 2020, following a suggestion of Artur Jasinski

Keywords

• nonn
• cons

Examples

			0.00409269829928628730747620468964025986524982473540016981249105600555721...
		

Crossrefs

Cf. A024006, A256919, A339529.

Programs

Mathematica

Join[{0, 0}, RealDigits[15/16 - Pi*Coth[Pi]/8 + Pi*(Sin[Sqrt[2]*Pi] + Sinh[Sqrt[2]*Pi]) / (4*Sqrt[2]*(Cos[Sqrt[2]*Pi] - Cosh[Sqrt[2]*Pi])), 10, 100][[1]]]

Formula

Equals Sum_{k>=2} 1/(k^8 - 1).

Equals 15/16 - Pi*coth(Pi)/8 + Pi * (sin(sqrt(2)*Pi) + sinh(sqrt(2)*Pi)) / (4*sqrt(2) * (cos(sqrt(2)*Pi) - cosh(sqrt(2)*Pi))).

Equals (1/2)*Sum_{k>=2} 1/(k^4-1) - (1/2)*Sum_{k>=2} 1/(k^4+1) = (A256919-A256920)/2. - R. J. Mathar, Jan 22 2021